Mercurial > octave-nkf
annotate scripts/general/interp3.m @ 8920:eb63fbe60fab
update copyright notices
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sat, 07 Mar 2009 10:41:27 -0500 |
| parents | fa78cb8d8a5c |
| children | 1bf0ce0930be |
| rev | line source |
|---|---|
| 8920 | 1 ## Copyright (C) 2007, 2008 David Bateman |
| 6702 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 6702 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 6702 | 18 |
| 19 ## -*- texinfo -*- | |
| 20 ## @deftypefn {Function File} {@var{vi} =} interp3 (@var{x}, @var{y},@var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}) | |
| 21 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{xi}, @var{yi}, @var{zi}) | |
| 22 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{m}) | |
| 23 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}) | |
| 24 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}) | |
| 25 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}, @var{extrapval}) | |
| 26 ## | |
|
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fa78cb8d8a5c
corrections for typos
Brian Gough<bjg@network-theory.co.uk>
parents:
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changeset
|
27 ## Perform 3-dimensional interpolation. Each element of the 3-dimensional |
| 6702 | 28 ## array @var{v} represents a value at a location given by the parameters |
| 29 ## @var{x}, @var{y}, and @var{z}. The parameters @var{x}, @var{x}, and | |
| 30 ## @var{z} are either 3-dimensional arrays of the same size as the array | |
| 31 ## @var{v} in the 'meshgrid' format or vectors. The parameters @var{xi}, etc | |
| 32 ## respect a similar format to @var{x}, etc, and they represent the points | |
| 33 ## at which the array @var{vi} is interpolated. | |
| 34 ## | |
| 7001 | 35 ## If @var{x}, @var{y}, @var{z} are omitted, they are assumed to be |
| 6702 | 36 ## @code{x = 1 : size (@var{v}, 2)}, @code{y = 1 : size (@var{v}, 1)} and |
| 37 ## @code{z = 1 : size (@var{v}, 3)}. If @var{m} is specified, then | |
| 7001 | 38 ## the interpolation adds a point half way between each of the interpolation |
| 6702 | 39 ## points. This process is performed @var{m} times. If only @var{v} is |
| 40 ## specified, then @var{m} is assumed to be @code{1}. | |
| 41 ## | |
| 42 ## Method is one of: | |
| 43 ## | |
| 44 ## @table @asis | |
| 45 ## @item 'nearest' | |
| 46 ## Return the nearest neighbour. | |
| 47 ## @item 'linear' | |
| 48 ## Linear interpolation from nearest neighbours. | |
| 49 ## @item 'cubic' | |
| 50 ## Cubic interpolation from four nearest neighbours (not implemented yet). | |
| 51 ## @item 'spline' | |
| 52 ## Cubic spline interpolation--smooth first and second derivatives | |
| 53 ## throughout the curve. | |
| 54 ## @end table | |
| 55 ## | |
| 56 ## The default method is 'linear'. | |
| 57 ## | |
| 58 ## If @var{extrap} is the string 'extrap', then extrapolate values beyond | |
| 59 ## the endpoints. If @var{extrap} is a number, replace values beyond the | |
| 6742 | 60 ## endpoints with that number. If @var{extrap} is missing, assume NA. |
| 6702 | 61 ## @seealso{interp1, interp2, spline, meshgrid} |
| 62 ## @end deftypefn | |
| 63 | |
| 64 function vi = interp3 (varargin) | |
| 65 method = "linear"; | |
| 6742 | 66 extrapval = NA; |
| 6702 | 67 nargs = nargin; |
| 68 | |
| 69 if (nargin < 1) | |
| 70 print_usage (); | |
| 71 endif | |
| 72 | |
| 7174 | 73 if (ischar (varargin{end})) |
| 74 method = varargin{end}; | |
| 6702 | 75 nargs = nargs - 1; |
| 7174 | 76 elseif (ischar (varargin{end-1})) |
| 77 if (! isnumeric (varargin{end}) || ! isscalar (varargin{end})) | |
| 6702 | 78 error ("extrapal is expected to be a numeric scalar"); |
| 79 endif | |
| 7174 | 80 extrapval = varargin{end}; |
| 81 method = varargin{end-1}; | |
| 6702 | 82 nargs = nargs - 2; |
| 83 endif | |
| 84 | |
| 7174 | 85 if (nargs < 3 || (nargs == 4 && ! isvector (varargin{1}) |
| 86 && nargs == (ndims (varargin{1}) + 1))) | |
| 87 v = varargin{1}; | |
| 6702 | 88 if (ndims (v) != 3) |
| 89 error ("expect 3-dimensional array of values"); | |
| 90 endif | |
| 6722 | 91 x = varargin (2:4); |
| 92 if (any (! cellfun (@isvector, x))) | |
| 93 for i = 2 : 3 | |
| 94 if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v)) | |
| 95 error ("dimensional mismatch"); | |
| 96 endif | |
| 97 x{i} = permute (x{i}, [2, 1, 3]); | |
| 98 endfor | |
| 99 x{1} = permute (x{1}, [2, 1, 3]); | |
| 100 endif | |
| 101 v = permute (v, [2, 1, 3]); | |
| 102 vi = ipermute (interpn (v, x{:}, method, extrapval), [2, 1, 3]); | |
| 7174 | 103 elseif (nargs == 7 && nargs == (2 * ndims (varargin{ceil (nargs / 2)})) + 1) |
| 104 v = varargin{4}; | |
| 6702 | 105 if (ndims (v) != 3) |
| 106 error ("expect 3-dimensional array of values"); | |
| 107 endif | |
| 6722 | 108 x = varargin (1:3); |
| 109 if (any (! cellfun (@isvector, x))) | |
| 110 for i = 2 : 3 | |
| 111 if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v)) | |
| 112 error ("dimensional mismatch"); | |
| 113 endif | |
| 114 x{i} = permute (x{i}, [2, 1, 3]); | |
| 115 endfor | |
| 116 x{1} = permute (x{1}, [2, 1, 3]); | |
| 117 endif | |
| 118 y = varargin (5:7); | |
| 119 if (any (! cellfun (@isvector, y))) | |
| 120 for i = 2 : 3 | |
| 121 if (! size_equal (y{1}, y{i})) | |
| 122 error ("dimensional mismatch"); | |
| 123 endif | |
| 124 y{i} = permute (y{i}, [2, 1, 3]); | |
| 125 endfor | |
| 126 y{1} = permute (y{1}, [2, 1, 3]); | |
| 127 endif | |
| 128 v = permute (v, [2, 1, 3]); | |
| 7174 | 129 vi = ipermute (interpn (x{:}, v, y{:}, method, extrapval), [2, 1, 3]); |
| 6702 | 130 else |
| 131 error ("wrong number or incorrectly formatted input arguments"); | |
| 132 endif | |
| 133 endfunction | |
| 134 | |
| 135 %!test | |
| 136 %! x = y = z = -1:1; | |
| 137 %! f = @(x,y,z) x.^2 - y - z.^2; | |
| 138 %! [xx, yy, zz] = meshgrid (x, y, z); | |
| 139 %! v = f (xx,yy,zz); | |
| 140 %! xi = yi = zi = -1:0.5:1; | |
| 141 %! [xxi, yyi, zzi] = meshgrid (xi, yi, zi); | |
| 142 %! vi = interp3(x, y, z, v, xxi, yyi, zzi); | |
| 143 %! [xxi, yyi, zzi] = ndgrid (xi, yi, zi); | |
| 144 %! vi2 = interpn(x, y, z, v, xxi, yyi, zzi); | |
| 145 %! assert (vi, vi2); |